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1、Lecture 15: public goods and externality Content Public goods Subscription Efficient provision of public goods Public choice Externality Whats externality? How to solute it? Whats the efficient condition with externality.Public goods SubscriptionExcludableNon-excludableRival Private goodsRegulated g
2、oods(?)Non-rivalClub goodsPublic goodsPublic goods Subscription Excludability is the property problem Rivality is the physical problem. Y.Barzel(1989), Public domain Price determined by the property. Public goods Efficient provision of public goods Discrete case: xi : private goods G: public goods g
3、i: is contribution to public goods ui(G,xi), utility functionPublic goods Discrete case: benchmark If providing the public goods will Pareto dominate non. So ri: the reservation price of i.Public goods Then will get: The sum of reservation price exceeds the cost of public goods, its efficient to pro
4、vide the public goods.Public goods But, can private provide it? Reflection function: If: Non cooperation equilibrium (0,0) Public goods Voting:Public goods Continuous case: Social welfare function: Public goods Continuous case: Benchmark: Public goods Samuelson condition:Public goods Private provisi
5、on By Kuhn-Tucker first order condition: See the fig.Public goods A Nash equilibrium: The equation holds for one i at least. If the utility is quasi-linear, then we have : If ,then 2 to be the free-rider.Public goods When there is no free-rider? For 1, OrPublic goods Let be the demand for public goo
6、ds of his wealth. We have: And in the same way, we got: Public goods If utility is quasi-linear, If , then and If , then Public goods Insufficient provision of public goods While, Let Then: For So Public goods Voting: Paradox of voting (Condorcet paradox) Single-peaked preference (i pay fraction si
7、for G), has a unique maximum. Majority rule and median voter. Bowen equilibrium Public goods Lindahl allocation: Everybody have a competitive market to buy the public goods: First order condition:Public goods Revealing mechanism of demand for public goods. How to reveal the pi? The Groves-Clarke Mec
8、hanism Each agent report a bid for the public good, bi. The public goods is provided if Each agent i receives a side-payment equal to the other bids ,if the public goods is provided.Public goods The Groves-Clarke MechanismExternality Whats externality? Private cost and social costSee the fig. Extern
9、ality Integration: internalize the externality. Pigovian taxesExternality The first Coase theorem: The first order condition: Its indifferent for or !Externality The second Coase theorem: If there is a transaction cost: Externality A compensation mechanism: The firms announce a Pigovian tax ti Firm
10、1 produces x and pays t2x tax , firm 2 receives t1x compensation. And both pay penalty on the difference between their tax rate, say Externality For this game have a Subgame perfect equilibrium if and only if: Second stage: firm 1: First stage: firm 1 Firm 2: So we get:Public goods Public goods Public goodsPrivate goodsPublic goodsPrivate goodsg1g2x1w1g2w1Private cost and social cost
